where \(\mu (|\psi \rangle )=(|\psi _0|^2, |\psi _1|^2, \cdots , |\psi _{n-1}|^2)^T\)  is the coherence vector. The coherence measure \(C_f\)  can be extended to mixed states by the convex roof construction [1]}, [2]}. The coherence of convex roof \(C_{c}\)  is given by
\(C_{c}(\rho )=\min \sum _k p_k {C_f}(|\psi _k\rangle ),\) 
